MinT - Best Known (51, 51+46, s)-Nets in Base 3

Best Known (51, 51+46, s)-Nets in Base 3

(51, 51+46, 52)-Net over F₃ — Constructive and digital

Digital (51, 97, 52)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (13, 36, 24)-net over F₃, using
  - net from sequence [i] based on digital (13, 23)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. digital (15, 61, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(51, 51+46, 64)-Net over F₃ — Digital

Digital (51, 97, 64)-net over F₃, using

t-expansion [i] based on digital (49, 97, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(51, 51+46, 462)-Net in Base 3 — Upper bound on s

There is no (51, 97, 463)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19265 722298 159616 222302 933103 799754 328842 132499 > 3⁹⁷ [i]